Sunday, September 09, 2007

(Non-)universal quantifiers

Many readers will recall Everett's argument that Pirahã had no universal quantifier because statements featuring what he had originally translated as "all" would generally be considered true even if a small part of the original had to be excepted. I'm not sure the conclusion follows (universal quantification could still be its prototypical meaning, for example), but if it does, then it could equally well be argued to be true of Darja; a lot of statements about "all" that I hear made here are ones which the speaker is perfectly aware (and accepting) of the existence of exceptions to, and it took me a while to go against my mathematical training and realise that when they said "all", they didn't mean it in the logicians' sense. Actually, I suspect the same is true of many idiolects of English. This was brought to mind by a little example I heard yesterday: hađa ybi` kŭll ħaja, bəṣṣəħħ əlfṭayəs ma ybi`š هذا يبيع كُلّ حاجة، بصّح الفطايس ما يبيعش "This guy sells everything, but hammers he doesn't sell."

5 comments:

I think it's quite generally true in English, and the other standard average European languages: "all" and its equivalents means "all the relevant instances in context", not logician's "all". Indeed, sentences containing "all" are quite likely to be about essences, or typicals, or masses, or what have you.

It would not astonish me to find that this was true of every language.

I agree with John: the English translation sounds completely unexceptionable to me. I think there's a subset of English speakers (and doubtless so for other languages) who have the (to me) bizarre notion that language should be "logical," and they cause all sorts of mischief.

"It would not astonish me to find that this was true of every language."

Me neither, or at least of every natural language. Languages designed to describe fictional or carefully restricted worlds, as in mathematics, can afford to have narrower semantics.

However, in English there is at least a fairly widespread idea that "all" has a normative, technical sense of "every instance without exception." In societies without a similar caste of teachers to spread this idea, even that may not be the case.